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Partial Differential Equations in Action

From Modelling to Theory

  • Textbook
  • © 2016

Overview

Authors:
  1. Sandro Salsa

    1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

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  • Addresses the interplay between theory and modeling in problems arising in the applied sciences
  • Focuses on ideas and connections to concrete applications, in order to promote readers’ intuition and feel for the subject
  • Offers a variety of examples from different perspectives in applied sciences

Part of the book series: UNITEXT (UNITEXT, volume 99)

Part of the book sub series: La Matematica per il 3+2 (UNITEXTMAT)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Introduction

    • Sandro Salsa
    Pages 1-16

  3. Diffusion

    • Sandro Salsa
    Pages 17-114

  4. The Laplace Equation

    • Sandro Salsa
    Pages 115-178

  5. Scalar Conservation Laws and First Order Equations

    • Sandro Salsa
    Pages 179-257

  6. Waves and Vibrations

    • Sandro Salsa
    Pages 259-346

  7. Elements of Functional Analysis

    • Sandro Salsa
    Pages 347-426

  8. Distributions and Sobolev Spaces

    • Sandro Salsa
    Pages 427-504

  9. Variational Formulation of Elliptic Problems

    • Sandro Salsa
    Pages 505-550

  10. Further Applications

    • Sandro Salsa
    Pages 551-580

  11. Weak Formulation of Evolution Problems

    • Sandro Salsa
    Pages 581-614

  12. Systems of Conservation Laws

    • Sandro Salsa
    Pages 615-656

  13. Back Matter

    Pages 657-686
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Keywords

About this book

The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) over the last several years at the Politecnico di Milano. These courses had a twofold purpose: on the one hand, to teach students to appreciate the interplay between theory and modeling in problems arising in the applied sciences, and on the other to provide them with a solid theoretical background in numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts. The first part, chapters 2 to 5, is more elementary in nature and focuses on developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. In turn the second part, chapters 6 to 11, concentrates on the development of Hilbert spaces methods for the variational formulation and the analysis of (mainly) linear boundary and initial-boundary value problems.The third edition contains a few text and formulas revisions and new exercises.

Authors and Affiliations

  • Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Sandro Salsa

About the author

Prof. Sandro Salsa, Dipartimento di Matematica, Politecnico di Milano, Italy.

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